시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 871 223 142 24.357%

문제

종빈이는 아주 큰 그룹의 총수다. 이 그룹은 1부터 N번까지의 번호로 구분할 수 있는 N개의 기업을 운영하고 있다. 현재 각 기업은 서로 독립적인 자체 컴퓨팅 및 통신센터를 가지고 있다.

어느 날 종빈이는 계열사의 CTO인 서현이에게 서비스 개선을 위해 각 기업의 서버를 네트워크로 연결하여 단일 통신센터에서 관리 가능한 클러스터 형태로 구성할 것을 제안했다. 종빈이의 제안을 들은 서현이는 다음과 같은 병합 과정을 고안해냈다.

  1. 클러스터 A를 제공하는 기존에 존재하는 센터 I를 고른다.
  2. 클러스터 B를 제공하는 기업 J를 고른다. B는 A가 아닌 임의의 클러스터이며, J는 센터가 아닐 수 있다.
  3. I와 J를 통신 라인으로 연결한다. 이때 기업 I와 J를 잇는 라인의 길이는 |I – J|(mod 1000)이다.
  4. 위 방식을 통해 클러스터 A와 B는 새로운 클러스터로 합쳐지며, 이 클러스터는 B의 센터에 의해 제공된다.

이러한 병합 과정을 거치던 중에, 각 기업에서 현재 센터까지 연결되는 라인의 길이가 총 얼마나 되는지에 관한 문의가 들어왔다. 서현이를 위해 병합하는 과정과 그 과정에서 통신센터와 각 기업을 잇는 라인의 길이를 구하는 프로그램을 작성해보자.

입력

입력은 여러 개의 테스트케이스로 주어진다. 입력의 첫 번째 줄에는 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스에는 기업의 수를 나타내는 N(4 ≤ N ≤ 20,000)이 주어진다. 다음은 몇 개의 줄에 걸쳐 아래 두 가지 종류의 명령어가 들어온다.

  • E I – 기업 I와 현재 I의 센터까지의 거리를 출력한다. 
  • I I J – 센터 I를 기업 J에 연결한다.

각 테스트케이스의 끝에는 단어 O가 주어진다. 각 테스트케이스에서 명령어의 총 개수는 200,000개를 넘지 않으며, 그중 I 명령어의 개수는 N개보다 작다.

출력

E 명령어가 들어올 때마다 한 줄에 해당 거리를 출력한다.

예제 입력 1

1
4
E 3
I 3 1
E 3
I 1 2
E 3
I 2 4
E 3
O

예제 출력 1

0
2
3
5
[{"problem_id":"3780","problem_lang":"0","title":"\ub124\ud2b8\uc6cc\ud06c \uc5f0\uacb0","description":"<p>\uc885\ube48\uc774\ub294 \uc544\uc8fc \ud070 \uadf8\ub8f9\uc758 \ucd1d\uc218\ub2e4. \uc774 \uadf8\ub8f9\uc740 1\ubd80\ud130 N\ubc88\uae4c\uc9c0\uc758 \ubc88\ud638\ub85c \uad6c\ubd84\ud560 \uc218 \uc788\ub294 N\uac1c\uc758 \uae30\uc5c5\uc744 \uc6b4\uc601\ud558\uace0 \uc788\ub2e4. \ud604\uc7ac \uac01 \uae30\uc5c5\uc740 \uc11c\ub85c \ub3c5\ub9bd\uc801\uc778 \uc790\uccb4 \ucef4\ud4e8\ud305 \ubc0f \ud1b5\uc2e0\uc13c\ud130\ub97c \uac00\uc9c0\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc5b4\ub290 \ub0a0 \uc885\ube48\uc774\ub294 \uacc4\uc5f4\uc0ac\uc758 CTO\uc778 \uc11c\ud604\uc774\uc5d0\uac8c \uc11c\ube44\uc2a4 \uac1c\uc120\uc744 \uc704\ud574 \uac01 \uae30\uc5c5\uc758 \uc11c\ubc84\ub97c \ub124\ud2b8\uc6cc\ud06c\ub85c \uc5f0\uacb0\ud558\uc5ec \ub2e8\uc77c \ud1b5\uc2e0\uc13c\ud130\uc5d0\uc11c \uad00\ub9ac \uac00\ub2a5\ud55c \ud074\ub7ec\uc2a4\ud130 \ud615\ud0dc\ub85c \uad6c\uc131\ud560 \uac83\uc744 \uc81c\uc548\ud588\ub2e4. \uc885\ube48\uc774\uc758 \uc81c\uc548\uc744 \ub4e4\uc740 \uc11c\ud604\uc774\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ubcd1\ud569 \uacfc\uc815\uc744 \uace0\uc548\ud574\ub0c8\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\ud074\ub7ec\uc2a4\ud130 A\ub97c \uc81c\uacf5\ud558\ub294 \uae30\uc874\uc5d0 \uc874\uc7ac\ud558\ub294 \uc13c\ud130 I\ub97c \uace0\ub978\ub2e4.<\/li>\r\n\t<li>\ud074\ub7ec\uc2a4\ud130 B\ub97c \uc81c\uacf5\ud558\ub294 \uae30\uc5c5 J\ub97c \uace0\ub978\ub2e4. B\ub294 A\uac00 \uc544\ub2cc \uc784\uc758\uc758 \ud074\ub7ec\uc2a4\ud130\uc774\uba70, J\ub294 \uc13c\ud130\uac00 \uc544\ub2d0 \uc218 \uc788\ub2e4.<\/li>\r\n\t<li>I\uc640 J\ub97c \ud1b5\uc2e0 \ub77c\uc778\uc73c\ub85c \uc5f0\uacb0\ud55c\ub2e4. \uc774\ub54c \uae30\uc5c5 I\uc640 J\ub97c \uc787\ub294 \ub77c\uc778\uc758 \uae38\uc774\ub294 |I &ndash; J|(mod 1000)\uc774\ub2e4.<\/li>\r\n\t<li>\uc704 \ubc29\uc2dd\uc744 \ud1b5\ud574 \ud074\ub7ec\uc2a4\ud130 A\uc640 B\ub294 \uc0c8\ub85c\uc6b4 \ud074\ub7ec\uc2a4\ud130\ub85c \ud569\uccd0\uc9c0\uba70, \uc774 \ud074\ub7ec\uc2a4\ud130\ub294 B\uc758 \uc13c\ud130\uc5d0 \uc758\ud574 \uc81c\uacf5\ub41c\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc774\ub7ec\ud55c \ubcd1\ud569 \uacfc\uc815\uc744 \uac70\uce58\ub358 \uc911\uc5d0, \uac01 \uae30\uc5c5\uc5d0\uc11c \ud604\uc7ac \uc13c\ud130\uae4c\uc9c0 \uc5f0\uacb0\ub418\ub294 \ub77c\uc778\uc758 \uae38\uc774\uac00 \ucd1d \uc5bc\ub9c8\ub098 \ub418\ub294\uc9c0\uc5d0 \uad00\ud55c \ubb38\uc758\uac00 \ub4e4\uc5b4\uc654\ub2e4. \uc11c\ud604\uc774\ub97c \uc704\ud574 \ubcd1\ud569\ud558\ub294 \uacfc\uc815\uacfc \uadf8 \uacfc\uc815\uc5d0\uc11c \ud1b5\uc2e0\uc13c\ud130\uc640 \uac01 \uae30\uc5c5\uc744 \uc787\ub294 \ub77c\uc778\uc758 \uae38\uc774\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud574\ubcf4\uc790.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uc785\ub825\uc758 \uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\ub294 \uae30\uc5c5\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 N(4&nbsp;&le; N &le; 20,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c\uc740 \uba87 \uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 \uc544\ub798 \ub450 \uac00\uc9c0 \uc885\ub958\uc758 \uba85\ub839\uc5b4\uac00 \ub4e4\uc5b4\uc628\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>E I &ndash; \uae30\uc5c5 I\uc640 \ud604\uc7ac I\uc758 \uc13c\ud130\uae4c\uc9c0\uc758 \uac70\ub9ac\ub97c \ucd9c\ub825\ud55c\ub2e4.&nbsp;<\/li>\r\n\t<li>I I J &ndash; \uc13c\ud130 I\ub97c \uae30\uc5c5 J\uc5d0 \uc5f0\uacb0\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc758 \ub05d\uc5d0\ub294 \ub2e8\uc5b4 O\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;<span style=\"font-family:Arial,&quot;Helvetica Neue&quot;,Helvetica,Tahoma,sans-serif\">\uac01 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc5d0\uc11c \uba85\ub839\uc5b4\uc758 \ucd1d \uac1c\uc218\ub294 200,000\uac1c\ub97c \ub118\uc9c0 \uc54a\uc73c\uba70, \uadf8\uc911 I \uba85\ub839\uc5b4\uc758 \uac1c\uc218\ub294 N\uac1c\ubcf4\ub2e4 \uc791\ub2e4.<\/span><\/p>\r\n","output":"<p>E \uba85\ub839\uc5b4\uac00 \ub4e4\uc5b4\uc62c \ub54c\ub9c8\ub2e4 \ud55c \uc904\uc5d0 \ud574\ub2f9 \uac70\ub9ac\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3780","problem_lang":"1","title":"Corporative Network","description":"<p>A very big corporation is developing its corporative network. In the beginning each of the N enterprises of the corporation, numerated from 1 to N, organized its own computing and telecommunication center. Soon, for amelioration of the services, the corporation started to collect some enterprises in clusters, each of them served by a single computing and telecommunication center as follow. The corporation chose one of the existing centers I (serving the cluster A) and one of the enterprises J in some other cluster B (not necessarily the center) and link them with telecommunication line. The length of the line between the enterprises I and J is |I &ndash; J|(mod 1000). In such a way the two old clusters are joined in a new cluster, served by the center of the old cluster B. Unfortunately after each join the sum of the lengths of the lines linking an enterprise to its serving center could be changed and the end users would like to know what is the new length. Write a program to keep trace of the changes in the organization of the network that is able in each moment to answer the questions of the users.<\/p>\r\n","input":"<p>Your program has to be ready to solve more than one test case. The first line of the input file will contains only the number T of the test cases. Each test will start with the number N of enterprises (5&le;N&le;20000). Then some number of lines (no more than 200000) will follow with one of the commands:<\/p>\r\n\r\n<ul>\r\n\t<li>E I &ndash; asking the length of the path from the enterprise I to its serving center in the moment;&nbsp;<\/li>\r\n\t<li>I I J &ndash; informing that the serving center I is linked to the enterprise J.<\/li>\r\n<\/ul>\r\n\r\n<p>The test case finishes with a line containing the word O. The I commands are less than N.<\/p>\r\n","output":"<p>The output should contain as many lines as the number of E commands in all test cases with a single number each &ndash; the asked sum of length of lines connecting the corresponding enterprise with its serving center.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Europe > Southeastern European Regional Contest > SEERC 2004 B번

  • 문제를 번역한 사람: Acka
  • 잘못된 조건을 찾은 사람: kb6912